Question

x − 5y = 16
–4x − 8y = –8

Answer 1

To solve the system of equations:

1. \( x - 5y = 16 \) (Equation 1)
2. \( -4x - 8y = -8 \) (Equation 2)

First, we'll simplify Equation 2. We can divide the entire equation by -4:

\[
\frac{-4x}{-4} + \frac{-8y}{-4} = \frac{-8}{-4}
\]
This simplifies to:

\[
x + 2y = 2 \quad (Equation \ 3)
\]

Now we have two equations:

1. \( x - 5y = 16 \) (Equation 1)
2. \( x + 2y = 2 \) (Equation 3)

Next, we can solve for \( x \) from Equation 3:

\[
x = 2 - 2y \quad (Equation \ 4)
\]

Now, we'll substitute Equation 4 into Equation 1:

\[
(2 - 2y) - 5y = 16
\]

Combine like terms:

\[
2 - 7y = 16
\]

Now, isolate \( y \):

\[
-7y = 16 - 2
\]
\[
-7y = 14
\]
\[
y = -2
\]

Now that we have \( y \), we can substitute it back into Equation 4 to find \( x \):

\[
x = 2 - 2(-2)
\]
\[
x = 2 + 4
\]
\[
x = 6
\]

So, the solution to the system of equations is:

\[
x = 6, \quad y = -2
\]

The solution can be written as the ordered pair \((6, -2)\).